Use your knowledge of angle pair relationships to write an equation and solve for x in the diagram.
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According to the given graph, those are corresponding angles that are always congruent. So, we can elaborate on the following
[tex]5x+7=9x-63[/tex]Now, we solve for x, first, we subtract 7 on each side.
[tex]\begin{gathered} 5x+7-7=9x-63-7 \\ 5x=9x-70 \end{gathered}[/tex]Then, we subtract 9x on each side
[tex]\begin{gathered} 5x-9x=9x-70-9x \\ -4x=-70 \end{gathered}[/tex]We divide the equation by -4
[tex]\begin{gathered} \frac{-4x}{-4}=\frac{-70}{-4} \\ x=\frac{35}{2} \end{gathered}[/tex]Therefore, the solution is 35/2.Related Questions
A tower casts a shadow that is 135 feet long. A person that is 5 ft - 3 in. casts a shadow that is 9 feet long. How tall is the tower?
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The person and its shadow make a triangle, and the same happens with the building and its shadow. Those two triangles are similar, which means the ratio of the corresponding sides are equal.
Before calculating the ratios, let's write the person height only with one unit. The relation between feet and inches is
[tex]\begin{gathered} 1ft=12in\text{.} \\ \Rightarrow3in.=0.25ft \end{gathered}[/tex]The height of the person is 5.25ft.
As I stated before, the ratio of the corresponding sides is equal because the triangles are similar, this means the ratio between the shadows is equal to the ratio between the heights. Let's call the height of the building as h
[tex]\frac{135}{9}=\frac{h}{5.25}[/tex]Solving for h
[tex]\begin{gathered} \frac{135}{9}=\frac{h}{5.25} \\ h=5.25\times\frac{135}{9}=5.25\times15=78.75 \\ \end{gathered}[/tex]The height of the building is 78.75 ft.
I’m struggling with this question. I don’t even know where to start
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The empirical rule
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
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Given,
[tex]\begin{gathered} \mu=100 \\ \sigma=10 \end{gathered}[/tex](a)% of people who have IQ between 70 and 130...
70 and 130 are 3 standard deviations of the mean.
[tex]\begin{gathered} 70=\mu-3\sigma \\ 70=100-3(10) \\ 70=70 \\ \text{and,} \\ 130=\mu+3\sigma \\ 130=100+3(10) \\ 130=130 \end{gathered}[/tex]So, that is 99.7% of the people.
Answer - 99.7%(b)% of people with IQ less than 90 or greater than 110
"90" and "110" are 1 standard deviation of the mean. So, according to the Empirical Rule, 68% of data fall between 1 standard deviation of the mean.
We want to know what % of data falls outside this 1 standard deviation. That will be:
100 - 68 = 32%
Answer - 32%(c)% of people with IQ greate than 120
From the diagram above, we see that the region that is greater than 120 is 2.35%
Answer - 2.35%Find the equation of the line through (-8,-1) with slope -1/2. Write your answer in general form.
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The point-slope equation is given by:
y - y' = m(x - x')
where
m = slope
(x', y') is a point that lies in the line
For our question we have:
m = -1/2
(x', y') = (-8, -1)
Let's plug that in the equation:
y - y' = m(x - x')
y - (-1) = -1/2(x - (-8) )
y + 1 = -1/2(x + 8)
y + 1 = -1/2x - 4
2y + 2 = -x - 8
x + 2y + 2 + 8 = 0
x + 2y + 10 = 0
Answer: the equation of the line is x + 2y + 10 = 0
The height of trapezium is 4cm & its area is 30cm^(2). If the greater of the two parallel sides is double the smaller side find the lengths of parallel sides.
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Let the smaller side be x cm. The greater side will be 2x cm. The height of the trapezium is given 4 cm. Now, the area of trapezium is given 30 cm^2.
The formula of area of the trapezium is given below:
[tex]A=\frac{1}{2}\times\text{ (sum of parallel sides)}\times\text{ height}[/tex]Substitute the given values in the formula:
[tex]\begin{gathered} A=30 \\ \Rightarrow\frac{1}{2}\times(2x+x)\times4=30 \\ \Rightarrow2(3x)=30 \\ \Rightarrow6x=30 \\ \Rightarrow x=5 \end{gathered}[/tex]So, the lengths of parallel sides are 5 cm and 2 x 5 = 10 cm.
Letrx)= x?. If r(x) = 4, find x2-24Both 2 and -2 are correctNone of the choices are correct.
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r(x) = x^2
If r(x) = 4
4 = x^2
Solve for x:
√4 = x
x = 2 and x= -2
Both 2 and -2 are correct
U sing the graphs below, identify g(g(–2)). Tix g(x)
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let's first calculate g(-2). Given the information in the graph
[tex]g(-2)=0[/tex]therefore g(g(-2))=g(0) and by the graph
[tex]g(0)=2[/tex]so g(g(-2))=2
A bucket is being filled with water. The graph below shows the water height (in mm) versus the time the water has been running (in seconds).Use the graph to answer the questions.(a)How much does the height of the water increase for each second the water is running?mm(b)What is the slope of the line?
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a) To find the change of the height of the water for each second the water is running you find the vertical change for 1 unit horizontal change.
You can see that in 1 second (horizontal change) the change in the height is 4mm (vertical change)
Answer: 4mmb) To find the slope of a line you use the next formula:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{\Delta vertical}{\Delta horizontal} \\ \\ m=\frac{4}{1}=4 \end{gathered}[/tex]Then, the slope of the line is 4Colin is making a 10-1b bag of trail mix for his upcoming backpacking trip. Ifchocolates cost $3.00 per pound and mixed nuts cost $6.00 per pound and Colin hasa budget of $5.40 per pound of trail mix, how many pounds of each should he use?
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We first create a system of equations that can represent the problem given.
We let x represent the amount of chocolates, in pounds, and y be the amount of mixed nuts, also in pounds. Colin has a total of 10-lb bag of trail mix. We can write an equation representing this as:
[tex]x+y=10[/tex]Chocolate costs $3.00 per pound while mixed nuts cost $6.00 per pound. Colin's total budget is around $5.40 per pound. This can be represented in equation as:
[tex]\begin{gathered} 3x+6y=10(5.40) \\ 3x+6y=54 \end{gathered}[/tex]Hence, we now have the system of equations written as:
[tex]\begin{gathered} x+y=10 \\ 3x+6y=54 \end{gathered}[/tex]Solve the system of equations using methods of elimination, as follows:
[tex]\begin{gathered} -3(x+y=10) \\ 3x+6y=54 \\ \\ -3x-3y=-30 \\ 3x+6y=54 \\ \\ 3y=24 \\ y=8 \end{gathered}[/tex][tex]\begin{gathered} x+8=10 \\ x=10-8 \\ x=2 \end{gathered}[/tex]Therefore, Colin used 2 pounds of chocolates and 8 pounds of mixed nuts for this 10-lb trail mix.
Calculate the area of the circle shown below.4 in Approximate Value_________Exact Value________(round your approximate answers to thehundredths)Circumference of the circle:_________ in?_________ in?
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The circumference formula is
[tex]C=\pi d[/tex]Where d = 4 and pi = 3.14.
[tex]C=3.14\cdot4\approx12.56in[/tex]Hence, the circumference is 12.56 inches, approximately. The exact value is 4pi.Which expression is equivalent to 4(n + 5)?4n24n4n + 94n + 20
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ANSWER
[tex]4n+20[/tex]EXPLANATION
We have to find the equivalent expression to:
[tex]4(n+5)_{}[/tex]To do this, we apply the distributive property. That is:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]Therefore, we have:
[tex]\begin{gathered} 4(n+5)=(4\cdot n)+(4\cdot5) \\ \Rightarrow4n+20 \end{gathered}[/tex]That is the answer.
2 x 46what is the answer
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2 x 46
Multiplying the above will give 92
How long is this side of the triangle?10 inches9 inches8 inches7 inches5(-4,4)(4,4)321-4 -3 -2 -101234
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8 inches (option C)
Explanation:To find the side of the triangle, we would apply the distance formula:
[tex]dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]The points: (-4, 4) and (4, 4):
[tex]x_1=-4,y_1=4,x_2=4,y_2\text{ = }4[/tex][tex]\begin{gathered} \text{distance = }\sqrt[]{(4-4)^2+(4-(-4))^2} \\ \text{distance = }\sqrt[]{0^2+(4+4)^2} \\ \end{gathered}[/tex][tex]\begin{gathered} \text{distance = }\sqrt[]{0+8^2}\text{ = }\sqrt[]{0+64} \\ \text{distance = }\sqrt[]{64} \\ \text{distance }=\text{ 8 inches (option C)} \end{gathered}[/tex]Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.The area of the shaded region is__(Round to four decimal places as needed.)
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Answer:
For z=0.54 the cumulative probability and percentile is approximately 70.54%, so in this case the answer is 0.7054
I got 3x but when I put it in the answer was wrong
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10.00 divided by 0.38
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(8.0 x 10%)/(2.0 x 106)
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Which equation best represents a line that is perpendicular to the graph? A. y = 1/4x - 1 B. y = -1/4x - 1 C. y = 4x + 4 D. y = -4x - 1
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ANSWER
C. y = 4x + 4
EXPLANATION
We want to find the line that is perpendicular to the graph.
To do that, we have to find the slope of the graph and find the equation that has a negative inverse slope to the graph.
Note: A linear equation is written generally as:
y = mx + c
where m = slope
The slope of the graph can be found by using formula:
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two points that lie on the graph.
Let us pick the points:
(x1, y1) = (0,1)
(x2, y2) = (4, 0)
The slope of the graph is therefore:
[tex]\begin{gathered} \text{slope = }\frac{\text{0 - 1}}{4\text{ - 0}} \\ \text{slope = -}\frac{1}{4} \end{gathered}[/tex]The negative inverse of -1/4 is 4.
Therefore, the correct option is Option C because that equation has a slope of 4.
Mrs. Mendoza purchased a 30-lb bag of oranges for $31.50. She could have purchased a 5-ib bag of oranges for $6.05. How much money did she save per pound by buyingthe 30-lb bag instead of six 5-lb bags?$0.16 per lb.$0.18 per lb$0.27 per lb.$0.31 per lb.None of these choices are correct.
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Non of the choices is correct
Mrs. Mendoza saved $0.175 per pound by buying the 30 lb bag instead of the 5 lb bag
Explanation:What Mrs. Meendoza purchased:
30 lb bag of oranges for $31.05
1 lb costs $1.035
She could have purchased:
5 lb bag of oranges for $6.05
1 lb would have cost $1.21
The difference between these is:
$1.21 - $1.035 = $0.175
She saved $0.175 per pound by buying the 30 lb bag instead of the 5 lb bag
Find the first term and the difference in an arithmetic sequence if the 100th term is 13 and the 200th term is 82. d = ______(simplify the answer using an integer or simplified fraction)
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We will have the following:
*First: We know that arithmetic sequences follow:
[tex]a_n=a_1+d(n-1)[/tex]*Second: From the information given we will have:
a100:
[tex]13=a_1+d(100-1)\Rightarrow13=a_1+99d[/tex]a200:
[tex]82=a_1+d(200-1)\Rightarrow82=a_1+199d[/tex]Then we will find the common difference:
[tex]d=\frac{82-13}{200-100}\Rightarrow d=\frac{69}{100}\Rightarrow d=0.69[/tex]So, the common difference is 0.69.
*Third: We determine the first term:
[tex]13=a_1+0.69(99)\Rightarrow_{}13=a_1+68.31[/tex][tex]\Rightarrow a_1=-55.31\Rightarrow a_1=-\frac{5531}{100}[/tex]So, the first term is -55.31.
2)Triangle LMN with vertices L(2, -8), M(12, 8), and N(14, 4): k = 1/2
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L' (1, -4)
M' (6, 4)
N' (7, 2)
Explanation:
2) Vetices of LMN:
L (2, -8)
M (12, 8)
N (14, 4)
sclae factor = k = 1/2
Applying the scale factor:
L' = 1/2(2, -8) = (1, -4)
M' = 1/2(12, 8) = (6, 4)
N' = 1/2(14, 4) = (7, 2)
Plotting the graph:
A random group of 100 male business managers was gathered together. Of them, 81 were wearing ties. What percent is this? Answer this with a number and the "%" symbol.
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Given:group of 100 male business managers was gathered together. Of them, 81 were wearing ties.
Find: percentage of this
Explanation: percentage of persons whose wearing ties are equal to
[tex]\frac{81}{100}\times100=81\%[/tex]Final answer: 81 percent is required answer.
Write the equation for the following function that represents a horizontal shift left 4 and avertical shrink by a factor of 2 on the parent function f (x) = x²?
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We are given the parent function f(x) = x^2.
We are tasked to find an equation for that function that represents a 4-unit horizontal shift to the left and a vertical shrink by a factor of 2.
First, let u shift the function horizontally. This means adjusting f(x) = x^2 to f(x) = (x - h)^2, where h is equal to the horizontal movement. Because we are moving the function 4 units to the left, then h = -4. So, the new function become f(x) = (x -(-4))^2 or f(x) = (x + 4)^2.
Next, let's shrink the function by a factor of 2. This means that the original y-values are halved. So f(x) = (x + 4)^2 must be transformed to f(x) = 1/2 (x + 4)^2.
The new equation is f(x) = 1/2 (x + 4)^2.
A prism has congruent parallelograms for bases. One pair of parallel sides of the parallelogram measure 12 feet and are 5 feet apart. The altitude of the prism is 13 feetFind the volume of the prism.
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The volume of the prism can be gotten using the formula
[tex]\begin{gathered} V_{\text{PRISM}}=\text{Base area}\times perpendicularheight \\ \text{the base is a parallelogram} \\ \text{Base area=base}\times height \\ \text{Base}=12ft \\ \text{height}=5ft \\ \text{perpendicular height=13ft} \end{gathered}[/tex]By substitution, we will have
[tex]\begin{gathered} V_{\text{PRISM}}=12ft\times5ft\times13ft \\ V_{\text{PRISM}}=780ft^3 \end{gathered}[/tex]Hence,
The volume of the prism is 780 cubic feet
Question:- Find the distance between the points A(4, -3) and B( -4,3). Please solve the question according to Co-ordinate Geometry.
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ANSWER
The distance is between point A(4, -3) and B( -4,3) is 10 units.
EXPLANATION
Given: A(4, -3) and B( -4,3).
To find the distance between the two points, we will use the formula below:
[tex]|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]From the points given,
x₁ = 4 y₁ = -3 x₂=-4 y₂=3
Substitute the formula into the equation and evaluate.
[tex]|AB|=\sqrt[]{(-4-4)^2+(3+3)^2}[/tex][tex]=\sqrt[]{(-8)^2+(6)^2}[/tex][tex]=\sqrt[]{64+36}[/tex][tex]=\sqrt[]{100}[/tex][tex]=10[/tex]
Hence, the distance is between point A(4, -3) and B( -4,3) is 10 units.
Simplify the algebraic expression: x(x + 3) + x(2x - 4) + 6A) 3x² +5B) 24-x²+6(C)3x²-x+6D) 3x²+x+6
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Answer:
C. 3x²-x+6
Explanation:
Given the algebraic expression:
[tex]x\left(x+3\right)+x\left(2x-4\right)+6[/tex]First, open the brackets:
[tex]\begin{gathered} =x(x)+x(3)+x(2x)-x(4)+6 \\ =x^2+3x+2x^2-4x+6 \end{gathered}[/tex]Next, rearrange to bring the like terms together:
[tex]=x^2+2x^2+3x-4x+6[/tex]Finally, combine the like terms:
[tex]=3x^2-x+6[/tex]The correct option is C.
2. Marty and Irene Benefield purchased 400 shares of airline stockyears ago. They paid a total of $8,484.55 for the stock. Lastweek they sold the stock for $19.50 per share and paid an onlinecommission of $19.95.a. What was the amount of the sale?b. What was the net sale?c. What was the profit or loss?
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Solution
Step 1:
Find the cost per share
[tex]\begin{gathered} Cost\text{ per share = }\frac{8484.55}{400} \\ =\text{ \$21.211375} \end{gathered}[/tex]Selling price = $19.5
[tex]Total\text{ selling price = 400 }\times\text{ \$19.50 = \$7800}[/tex]a)
Amount of sale = $7800
b)
Net sale = Amount of sale - Commission
[tex]\begin{gathered} Net\text{ sale = \$7800 - \$19.95} \\ =\text{ \$7780.05} \end{gathered}[/tex]c) Amount paid = $8484.55
Net sale = $7780.05
Since net sale is less than the amount paid, hence, it is loss
Loss
5- 1 5=-4 7 1 ==4= (Type a whole number, fraction, or mixed number.)
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we have
[tex]5\frac{1}{7}\colon4[/tex]convert mixed number to an improper fraction
5 1/7=5+1/7=36/7
substitute
(36/7)/4=36/(7*4)=9/7
answer is 9/7
convert to mixed number
9/7=7/7+2/7=1+2/7=
A certain triangle has a perimeter of 3084 mi. The shortest side measures 76 mi less than the middle side, and the longest side measures 379 mi more than the middle side. Find the lengths of the three sides.
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shortest side: 851
middle side:927
longest side : 1306
Explanation
Step 1
Let
x represents the shortest side
y represents the middle side
z represents the longest side
so, set the equations
a) the perimeter of a rectangle is the sum of the sides, so
[tex]\begin{gathered} \text{Perimeter= side1+side2+side3} \\ replace \\ 3084=x+y+z \\ x+y+z=3084\Rightarrow\text{ Equation(1)} \end{gathered}[/tex]b) The shortest side measures 76 mi less than the middle side( in other words, you have to subtract 76 from middle side to get the shortest side)
[tex]x=y-76\Rightarrow equation(2)[/tex]c) and the longest side measures 379 mi more than the middle side,( in other words, you have to add 379 to middle side to obtain the longest side)
[tex]z=y+379\Rightarrow equation(3)[/tex]Step 2
solve the equations
a) now, replace the x an z value sfrom equation (2) and (3) into equation(1)
[tex]\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ (y-76)+y+(y+379)=3084 \\ -76+3y+379=3084 \\ 303+3y=3084 \\ 3y=3084-303 \\ \\ 3y=2781 \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{2781}{3} \\ y=927 \end{gathered}[/tex]now, replace the y value in equatino (2) to find x
b)
[tex]\begin{gathered} x=y-76\Rightarrow equation(2) \\ x=927-76 \\ x=851 \end{gathered}[/tex]c) finally, prelace x and y value in equation (1) to find z
[tex]\begin{gathered} x+y+z=3084\Rightarrow\text{ Equation(1)} \\ 851+927+z=3084 \\ \text{add like terms} \\ 1778+z=3084 \\ \text{subtract 1778 in both sides} \\ 1778+z-1778=3084-1778 \\ z=1306 \end{gathered}[/tex]so
shortest side: 851
middle side:927
longest side : 1306
I hope this helps you
The solar system started 4.6 billion years old. You are measuring the amount of calcium in the rock sample to determine if the rock was from the start of our solar system. Calcium has a half life of 1.25 billion years. The rock that you have found has experienced 3.6 half lives. QUESTION: is the rock likely a meteorite from the start of the solar system?
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Half-life of a rock = 1.25 billion years
Rock lives of the rock found = 3.6 half-lives
Multiply the number of billion years of each half live (1.25) by the number of half-lives of the rock found:
1.25 x 3.6 = 4.5 billion years
Since the solar system started 4.6 billion years ago, the rock found is not from the start of the solar system.
Let BD bisect 2ABC. If m_ABD =(3x+8) and m DBC =(7x+4), then what is the measure of ABD?
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Note a bisector divide an angle into 2 equal half.
